Mapping class groups of manifolds of dimension four and higher can be rather wild: for instance, \(\operatorname{Map}({\mathbb {S}}^1 \times {\mathbb {S}}^3)\)  is not finitely generated [1]}, and the same holds for the mapping class group of the \(n\) -dimensional torus, for \(n\ge 6\)  (see e.g. [2]}). However, Sullivan proved the following striking result [3]}:
